Directional emissions of light-pulses from a point-source (which is stationary at the origin of a moving inertial reference-frame) towards detectors which are all stationary at a constant radial-distance from the light-source (within the latter's inertial reference-frame) are transformed
into another time-synchronized inertial reference-frame relative to which the source is moving with a speed v. Both the Galilean-transformation and the Lorentz-transformation are used. Light-pulses along different directions are compared to the equivalent situation when a spherical wavefront
is emitted from the same source. The Galilean-transformation gives transformed coordinates of points on this wavefront that remain coincident on this wavefront; which, in turn, remains centered at the origin of the moving inertial reference-frame. In contrast, the Lorentz-transformation mandates
that the same spherical wavefront must be observed as twin wavefronts, each of which remains centered at one of the origins of the moving and the stationary reference-frames, respectively. Here it is found that the Lorentz-transformation of simultaneous-instantaneous position-coordinates,
of points on the wavefront within the moving inertial reference-frame, does not result in points which are simultaneously situated on its twin wavefront within the stationary inertial reference-frame. This is a compelling proof that an event which occurs at nonzero position-coordinates and
at a nonzero time within the moving inertial reference-frame is not observed coincidently from the origin of another time-synchronized inertial reference-frame relative to which the reference-frame of the source is moving.

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